Numerical method for solving fractional convection diffusion equations with time-space variable coefficients

This paper contributes a numerical method for solving a class of fractional convection diffusion equations with time-space variable coefficients. By implementing Legendre polynomials and also the associated operational matrix, the considered equations will be reduced to the corresponding systems of algebraic equations, which can be solved by computer programming. Also, the error analysis of the suggested method to the exact solutions is provided. Finally, numerical examples are provided to show the efficiency of the presented method.